The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If…
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20\text{ cm}$, the length of the open organ pipe is [NEET 2018]
12.5 cm
8 cm
13.3 cm
16 cm
Solution
Fundamental frequency for an open organ pipe is given as
$f = \frac{v}{2L}$
where, $L$ is the length of the open organ pipe.
Third harmonic for a closed organ pipe is given as $f' = \frac{3v}{4L'}$
where, $L'$ is the length of closed organ pipe.
According to the question, $f = f'$
$\frac{v}{2L} = \frac{3v}{4L'}$
$\Rightarrow L = \frac{2}{3}L'$
Given, $L' = 20\text{ cm}$
$\Rightarrow L = \frac{2}{3} \times 20\text{ cm} = \frac{40}{3}\text{ cm} = 13.3\text{ cm}$